Question

A tangent galvanometer has 80 turns of wire. The internal and external diameters of the coil are 19 cm and 21 cm respectively. The reduction factor of the galvanometer at a place where H=0.32 oersted will be (1 oersted= $80\text{ A}{{\text{m}}^{-1}}$)

Answer 1

Hint: A tangent galvanometer is a small electric current measurement device. It's made up of a coil of insulated copper wire wrapped around a non-magnetic circular frame. It's operation is founded on the theory of magnetism's tangent rule. A magnetic field (B) is formed at the center of the circular coil when a current is passed through it in a direction perpendicular to the coil's plane. The horizontal portion of the earth's magnetic field is directed in the direction of the plane of the coil in the Tangent Galvanometer.

Complete step by step solution:
In this question we have been given that
Internal Radius ${{R}_{i}}=\dfrac{D}{2}=\dfrac{19}{2}=9.5\text{ cm or 0}\text{.095 m}$
External Radius ${{R}_{e}}=\dfrac{D}{2}=\dfrac{21}{2}=10.5\text{ cm or 0}\text{.105 m}$
The average radius is $R=\dfrac{{{R}_{i}}+{{R}_{e}}}{2}=\dfrac{0.095+0.105}{2}=0.1\text{ m}$
Also ${{B}_{H}}={{\mu }_{0}}H$
And H=0.32 oersted or we can write $H=0.32\times 80=25.6\text{ A}{{\text{m}}^{-1}}$
Now, the Reduction Factor is given by
$k=\dfrac{2R({{B}_{H}})}{N{{\mu }_{0}}}$
Where “K” is the reduction factor
N = number of turns of wire
Putting the values, we get
$k=\dfrac{2(0.1)({{\mu }_{0}}25.6)}{(80){{\mu }_{0}}}$
On solving this, we get
K = 0.064
Hence, this is the required solution

Note: A galvanometer is an electric current measurement instrument that is electromechanical. Early galvanometers were uncalibrated, but later models, known as ammeters, were calibrated and could more accurately calculate current flow. A galvanometer responds to an electric current flowing through a coil in a continuous magnetic field by deflecting a pointer. Galvanometers have played an important role in the advancement of science and technology in a variety of fields. For example, in the 1800s, they facilitated long-distance communication through submarine cables, such as the first transatlantic telegraph cables, and their fine current measurements were crucial in discovering the electrical activity of the heart and brain.